Computation Section
Subunit Inventory Analysis
 O/I Ratios

In many situations the flow that enters a component may be different that the flow that leaves it. An example is an inspection operation in a manufacturing plant. The parts entering the inspection are discarded if they are found faulty and the flow passed to the next operation is less than the flow entering the inspection. In this case the O/I ratio is less than 1. Alternatively, the operation may divide an assembly into several subassemblies. Here the flow entering is less than the flow leaving and the O/I ratio is greater than 1.

When the O/I ratio box is checked extra rows are added to the display to hold the ratio information. The line structure has several new rows, while the tree an network structure have one additional row. Formulas for computing the operation flows are adjusted to correctly account for the ratios.

The example used on the System page is shown below as it is constructed with the ratio button checked. The example is a pull line, so we see several new rows at the bottom of the display. We use the same data as previously, but add some non-unity ratios. This example does not represent any reality, but it does illustrate the effect of ratios on flow.

The extra rows starting in row 21 first list the indices for the components, then repeat their names. Row 23 holds the amount pulled from each component. This is a new feature for the line structure and it can be used to pull intermediate flow from any component. The example pulls 100 units from component 7 and all other flows are based on this amount.

Row 24 holds the O/I ratios for the components. Note that components 4 and 5 each have the value of 0.9. This means for every unit that enters each operation, 0.9 will leave. The flow rates are adjusted accordingly in row 25. Because the flow leaving operation 5 is 100, the flow entering must be 100/0.9 or 111.11. Similarly, the flow entering operation 4 must be 111.11/0.9 or 123.46. The flows are computed with Excel formulas in the Flow Rate cells in row 25.

There are several features that should be recognized. We have not changed the lot sizes to reflect the flow changes. For example, the flow enters operation 5 in lots of 6 and leaves in lots of 3. Since more flow enters due to the ratio, the lots must arrive more frequently than if the ratio were 1. The total flow shown in cell I23 is not the same as the flow in each component. Since the system cycle time is computed with this value, the system cycle time is not the time for a finished unit to pass through the system, but it is an adjusted time that also reflects units that start but do not finish.

In the following we illustrate the several drive/structure options when ratios are allowed to be other than 1. These are the same examples used to illustrate the options without ratios, however, some of the ratios have been changed to illustrate the effect.




For the push line, the ratios change the flows as they pass down the line. Since the ratios for the example are less than 1, the flow decreases as the material progresses down the line. The flow that starts at operation 1 at 100 leaves the system at 81.

With non-unity ratios, the push and pull lines are no longer symmetric. The example below shows the same parameters but is a pull line. For the pull line with ratios less than 1, the flow in the earlier operations must increase to accommodate the losses.

Pull Tree




We change the example given earlier by adding ratios for the process and batch operations. Note that ratios may be any positive number. A ratio of 0 or a negative ratio will cause an error.

Push Tree



The O/I ratios represent losses in the queuing network. Not all that is shipped from the depot reaches the local distributors.

Pull Network



The ratios represent losses due to defects in the manufacturing process. The flows through the processes and the raw material requirements are increased. The ratios affect the augmented matrix and subsequently the flows through the processes.

Push Network


For the doctor's office the ratios might represent patients who might leave because of the graphic nature of the movie or patients who don't survive the treatment. Not everyone who arrives will pay. The ratios do not affect the transfer matrix, but they do affect the augmented matrix.

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tree roots

Operations Management / Industrial Engineering
by Paul A. Jensen
Copyright 2004 - All rights reserved